A first-order explicit Euler integrator of (REF ) has oscillation when \(1-T_sD_{i}M^{-1}_{i}<0\)  [1]}, where \(\bullet _{i}\)  denotes the \(i,i\) -th element of a matrix. Instead, we use the semi-implicit integration of [2]} on (REF ) to find
\(\begin{aligned}\mathbf {\xi }_{t+1} &= \begin{bmatrix} \mathbf {I} && T_s \mathbf {I} \\ \mathbf {0} && \mathbf {M}\left(\mathbf {M}+T_s\mathbf {D}\right)^{-1}\end{bmatrix}\mathbf {\xi }_t \\& \qquad + \begin{bmatrix} \mathbf {0} \\ T_s\mathbf {M}^{-1} \end{bmatrix}(\mathbf {f}_t-\mathbf {f}_t^r),\end{aligned}\) 
